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Week of...

Notes and Links

1

Jan 9

Tuesday Hour 1: Course introduction as in About This Class (pdf, html). Tuesday Hour 2: The Jones polynomial via the Kauffman bracket, following 170110JonesPoly.nb (preclass: pdf, nb; postclass: pdf, nb). Friday: Knots, algebras, YangBaxter, CYBE, Lie algebras, universal enveloping algebras, formulas.

2

Jan 16

Tuesday Hour 1: More on the Jones polynomial via the Kauffman bracket, following 170117MoreJones.nb (preclass: pdf, nb; postclass: pdf, nb). Tuesday Hour 2: Continuation, 170117FastSlowRace.nb (preclass: pdf, nb; postclass: pdf, nb), knot genus. Friday: The Lie algebra following 170120g0.nb (preclass: pdf, nb; postclass: pdf, nb).

3

Jan 23

Tuesday Hour 1: Tangles and metamonoids. Tuesday Hour 2: The fundamental group, metaHopf algebras, algebraic knot theory. Friday: The Lie algebra following 170127g0.nb (preclass: pdf, nb; postclass: pdf, nb). Class Photo.

4

Jan 30

Tuesday Hour 1: Tangles, links, and 3manifolds. Tuesday Hour 2: Genus, ribbon, slice. Friday: Normal orderings following 170203g0dsO.nb (preclass: pdf, nb; postclass: pdf, nb).

5

Feb 6

Tuesday Hour 1: calculus following 170207GammaCalculus.nb (preclass: pdf, nb; postclass: pdf, nb), part I. Tuesday Hour 2: calculus following 170207GammaCalculus.nb (preclass: pdf, nb; postclass: pdf, nb), part II. Friday: The main theorem following 170210g0MainTheorem.nb (preclass: pdf, nb; postclass: pdf, nb).

6

Feb 13

Tuesday Hour 1: Expansions in general; also using 170214ProgressiveScanning.nb (preclass: pdf, nb; postclass: pdf, nb). Tuesday Hour 2: Expansions for tangles, finite type invariants. Friday: Computing the invariant following 170217g0Invariant.nb (preclass: pdf, nb; postclass: pdf, nb).

R

Feb 20

Reading Week.

7

Feb 27

Tuesday Hour 1: Expansions and the fundamental theorem for . Tuesday Hour 2: Algebraic structures on . Friday: Conclusion of the discussion following 170303g0LemmaAndInvariant.nb (preclass: pdf, nb; postclass: pdf, nb).

8

Mar 6

Tuesday Hour 1: The polished invariant following 170307g0Polished.nb (preclass: pdf, nb; postclass: pdf, nb) and lemmas following 170307geps.nb (preclass: pdf, nb; postclass: pdf, nb). Tuesday Hour 2: The logos for following 170307geps.nb (preclass: pdf, nb; postclass: pdf, nb). Friday: Algebraic structures on , trivalent diagrams.

9

Mar 13

Monday is the last day to drop this class. Friday: Deriving and testing the Logos following 170317g1Invariant.nb (preclass: pdf, nb; postclass: pdf, nb) and 170317TestingTheLogos.nb (preclass: pdf, nb; postclass: pdf, nb).

10

Mar 20

Tuesday Hour 1: The invariant following 170321g1Invariant.nb (preclass: pdf, nb; postclass: pdf, nb) and 170321Polishedg1Invariant.nb (preclass: pdf, nb; postclass: pdf, nb). Tuesday Hour 2: offline, though see BBS/AKT17170321145350.jpg and BBS/AKT17170321150540.jpg. Friday: Associators, also following 170324Associator.nb (preclass: pdf, nb; postclass: pdf, nb) and 170324MutipleZetaValues.pdf.

11

Mar 27

Classes canceled due to an MSRI workshop.

12

Apr 3

Tuesday Hour 1: Diagrams to Universal Enveloping Algebras, the ucase. Tuesday Hour 2: Virtual knots and diagrams to Universal Enveloping Algebras, the vcase. Friday: Sjabbo Schaveling: The Quantum Double towards , following 170407Classical_Algebra_E0.nb (pdf, nb), 170407Quantum_Algebra_E0.nb (pdf, nb), and 170407E_machten_Algebra_E0_v2.nb (pdf, nb).

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Dror's Notebook



Algebraic Knot Theory  PolyTime Computations
Department of Mathematics, University of Toronto, Spring 2017
Agenda. Groupdiscover and groupimplement the strongest ever truly computable knot invariant; along the way, learn some of the why (topology!), what (Lie theory!), and how (Mathematica!). Leave behind a complete documentation trail.
Alternatively, "understand everything in http://drorbn.net/GWU1612/, and beat it".
Instructor: Dror BarNatan, drorbn@math.toronto.edu, Bahen 6178, 4169465438. Office hours: by appointment.
Classes. Tuesdays 111 and Fridays 1112 at Bahen 6180. Also a "HW meeting", covering no new material, on Fridays at 6:10PM at or near my office.
About This Class (pdf, html).